Hypergeometric method for Klein-Gordon equation with trigonometric Pöschl-Teller and trigonometric Scarf II potentials

The Hypergeometric method was used to solve the Klein-Gordon equation with Trigonometric Pöschl-Teller and Trigonometric Scarf II potentials. By using variable and parameter substitutions, Klein-Gordon equation for spin symmetry case was reduced into second-order differential equation. The radial part of Klein-Gordon equation with radial trigonometric Pöschl-Teller potentials was solved in the scheme of centrifugal approximation by using hypergeometric method. The relativistic energy equation was obtained and calculated numerically by using Matlab R2013 software. On the other hand, wave function equation was obtained and visualized by Matlab R2013 software. The energy value depends on n, k, and μ values, while the quantum number and mass have effect for distribution of particle in visualization of wave function.